d/dx[cscx]
To find the derivative of csc(x) with respect to x, we can use the chain rule and the derivative of sin(x)
To find the derivative of csc(x) with respect to x, we can use the chain rule and the derivative of sin(x).
Recall that csc(x) is equal to 1/sin(x), so we can rewrite the expression as:
csc(x) = 1/sin(x)
Now, let’s find the derivative.
We can start by rewriting csc(x) as:
csc(x) = (sin(x))^(-1)
Using the power rule, the derivative of (sin(x))^(-1) would be:
d/dx[(sin(x))^(-1)] = -1 * (sin(x))^(-2) * cos(x)
Now, we just need to substitute sin(x) back into the expression. Recall that:
sin(x) = 1/csc(x)
Substituting sin(x) in terms of csc(x), we get:
d/dx[(sin(x))^(-1)] = -1 * (1/csc(x))^(-2) * cos(x)
Simplifying further:
d/dx[csc(x)] = -cos(x)/(csc(x))^2
Therefore, the derivative of csc(x) with respect to x is -cos(x)/(csc(x))^2.
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